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By intervention I mean some external agent causing the system to leave the initial equilibrium macrostate A, which would not happen spontaneously. E.g. a wall i

by effie 4y ago

By intervention I mean some external agent causing the system to leave the initial equilibrium macrostate A, which would not happen spontaneously. E.g. a wall is removed, or a piston is quickly pushed, to make the system evolve towards new equilibrium macrostate. > given a set of measurement values, the more states there are which produce those values, the more likely we are, all else being equal, to observe those values. And so a closed system will evolve by pure chance into a state where the entropy is maximized simply because you are more likely to observe values corresponding to greater numbers of underlying states. This argument is that future macrostates of an isolated system passing through non-equilibrium states (due to some intervention to the system that was in an equilibrium state before) should be almost always of higher entropy, because those have immensely higher multiplicity than macrostates with lower entropy. There is hugely more microstates that are compatible with higher entropy macrostate, than microstates that are compatible with lower entropy macrostate. However notice the word "future". We can formulate the same argument using "past": past macrostates of an isolated system passing through non-equilibrium states should be almost always of higher entropy, because those have immensely higher multiplicity than macrostates with lower entropy. There is hugely more microstates that are compatible with higher entropy macrostate, than microstates that are compatible with lower entropy macrostate. Now, why does the argument give correct answer when applied to future macrostates but not when applied to past macrostates? We need additional assumption about the non-equilibrium process that makes the argument invalid for the past.

lisper 4y ago
> By intervention I mean some external agent causing the system to leave the initial equilibrium macrostate OK, that's what I thought. > We need additional assumption about the non-equilibrium process that makes the argument invalid for the past. Ah. No, you don't need any additional assumptions. All you need is to observe that the present constrains the past differently from the future. There are fewer pasts compatible with a given present than there are futures compatible with that same present. You can't just say that there are many high-entropy microstates, and so you are as likely to encounter one in the past as you are in the future, because any candidate past state has to be able to evolve into the present state. And if the present state is a low-entropy state, the precursor for that is much more likely to be an even lower-entropy state. Yes, there are high-entropy microstates that will evolve into low-entropy ones, but the fraction of those states chosen from among all high-entropy microstates is indistinguishable from zero, and so the odds of a high-entropy microstate in general being the precursor of a present low-entropy state is likewise indistinguishable from zero. By way of very stark contrast, the successor states of a low-entropy state (or any state for that matter) is much more likely to be a high entropy state than a low-entropy one for the exact same reason: the present constrains the past more rigidly than it does the future.
- effie 4y ago
  > you don't need any additional assumptions What you wrote after that is such an assumption. You can't derive asymmetry from nothing, logic or mechanics. The only way to have it, is to assume it in addition to those.
  - lisper 4y ago
    > What you wrote after that is such an assumption. Not quite. There is an underlying assumption, but that's not it. I can demonstrate the asymmetry between the past and future. For example: Suppose I flip a fair coin, and I make a video of the coin flip. Let's say the coin comes up heads. I can predict with near 100% certainty (modulo shenanigans) that if I watch the video I will see a coin being flipped and coming up heads. By way of very stark contrast, I cannot predict the outcome of actually flipping the coin again with better than 50% odds. I claim that this asymmetry in my prophetic abilities (100% ability to predict what will be seen on the video vs 50% for re-flipping the actual coin) is a result of the asymmetry between the past and future. Note that this is not a circular argument; this demonstration would work equally well in a universe where it is possible to unscramble an egg. All it requires is for there be some experiment whose outcome I can record but not predict, even with arbitrarily advanced technology. The existence of such an experiment is an assumption, but it is a very weak assumption, much weaker than the second law itself. Indeed, it is a necessary assumption for doing thermodynamics at all, indeed, for doing anything. If I can reliably predict the outcome of any experiment, that means I know everything that is going to happen before it happens, including my own actions. So yes, I have to assume that I cannot be omniscient. Or maybe a better word here would be "hope" because being omniscient would render my entire existence meaningless.
    - effie 4y ago
      > I claim that this asymmetry in my prophetic abilities (100% ability to predict what will be seen on the video vs 50% for re-flipping the actual coin) is a result of the asymmetry between the past and future. No, this and other similar memory-induced asymmetries have much more prosaic reason. It is more successful to predict systems we have enough knowledge and control of (video playback) than those we don't (coin flip). Predicting and retrodicting systems we understand and have memory of is successful, and predicting and retrodicting systems we don't understand and don't have memory of is not. This has nothing to do with universal asymmetry of past vs future. Your memory of what has happened (e.g. some system had lower entropy in past) does not explain why your original argument does not apply now to retrodiction of past macrostates; the memory only contradicts the result of that argument. > If I can reliably predict the outcome of any experiment, that means I know everything that is going to happen before it happens, including my own actions. That would in no way prevent validity of 2nd law.

by effie 4y ago

lisper 4y ago

> By intervention I mean some external agent causing the system to leave the initial equilibrium macrostate OK, that's what I thought. > We need additional assumption about the non-equilibrium process that makes the argument invalid for the past. Ah. No, you don't need any additional assumptions. All you need is to observe that the present constrains the past differently from the future. There are fewer pasts compatible with a given present than there are futures compatible with that same present. You can't just say that there are many high-entropy microstates, and so you are as likely to encounter one in the past as you are in the future, because any candidate past state has to be able to evolve into the present state. And if the present state is a low-entropy state, the precursor for that is much more likely to be an even lower-entropy state. Yes, there are high-entropy microstates that will evolve into low-entropy ones, but the fraction of those states chosen from among all high-entropy microstates is indistinguishable from zero, and so the odds of a high-entropy microstate in general being the precursor of a present low-entropy state is likewise indistinguishable from zero. By way of very stark contrast, the successor states of a low-entropy state (or any state for that matter) is much more likely to be a high entropy state than a low-entropy one for the exact same reason: the present constrains the past more rigidly than it does the future.

effie 4y ago
> you don't need any additional assumptions What you wrote after that is such an assumption. You can't derive asymmetry from nothing, logic or mechanics. The only way to have it, is to assume it in addition to those.
- lisper 4y ago
  > What you wrote after that is such an assumption. Not quite. There is an underlying assumption, but that's not it. I can demonstrate the asymmetry between the past and future. For example: Suppose I flip a fair coin, and I make a video of the coin flip. Let's say the coin comes up heads. I can predict with near 100% certainty (modulo shenanigans) that if I watch the video I will see a coin being flipped and coming up heads. By way of very stark contrast, I cannot predict the outcome of actually flipping the coin again with better than 50% odds. I claim that this asymmetry in my prophetic abilities (100% ability to predict what will be seen on the video vs 50% for re-flipping the actual coin) is a result of the asymmetry between the past and future. Note that this is not a circular argument; this demonstration would work equally well in a universe where it is possible to unscramble an egg. All it requires is for there be some experiment whose outcome I can record but not predict, even with arbitrarily advanced technology. The existence of such an experiment is an assumption, but it is a very weak assumption, much weaker than the second law itself. Indeed, it is a necessary assumption for doing thermodynamics at all, indeed, for doing anything. If I can reliably predict the outcome of any experiment, that means I know everything that is going to happen before it happens, including my own actions. So yes, I have to assume that I cannot be omniscient. Or maybe a better word here would be "hope" because being omniscient would render my entire existence meaningless.
  - effie 4y ago
    > I claim that this asymmetry in my prophetic abilities (100% ability to predict what will be seen on the video vs 50% for re-flipping the actual coin) is a result of the asymmetry between the past and future. No, this and other similar memory-induced asymmetries have much more prosaic reason. It is more successful to predict systems we have enough knowledge and control of (video playback) than those we don't (coin flip). Predicting and retrodicting systems we understand and have memory of is successful, and predicting and retrodicting systems we don't understand and don't have memory of is not. This has nothing to do with universal asymmetry of past vs future. Your memory of what has happened (e.g. some system had lower entropy in past) does not explain why your original argument does not apply now to retrodiction of past macrostates; the memory only contradicts the result of that argument. > If I can reliably predict the outcome of any experiment, that means I know everything that is going to happen before it happens, including my own actions. That would in no way prevent validity of 2nd law.